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Damping Matrices (damping + matrix)

Distribution by Scientific Domains

Engineering	100%

Selected Abstracts

Experimental study of the semi-active control of building structures using the shaking table

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 15 2003
Qing Sun
Abstract A magnetorheological (MR) damper has been manufactured and tested and a non-linear model is discussed. The parameters for the model are identified from an identification set of experimental data; these parameters are then used to reconstruct the force vs. displacement and the force vs. velocity hysteresis cycles of the MR damper for the hysteretic model. Then experiments are conducted on a three-storey frame model using impact excitation, which identifies dynamic parameters of the model equipped with and without the MR damper. Natural frequencies, damping ratios and mode shapes, as well as structural properties, such as the mass, stiffness and damping matrices, are obtained. A semi-active control method such as a variable structure controller is studied. Based on the ,reaching law' method, a feedback controller is presented. In order to evaluate the efficiency of the control system and the effect of earthquake ground motions, both numerical analysis and shaking table tests of the model, with and without the MR damper, have been carried out under three different ground motions: El Centro 1940, Taft 1952, and Ninghe 1976 (Tangshan Earthquake in Chinese). It is found from both the numerical analysis and the shaking table tests that the maximum accelerations and relative displacements for all floors are significantly reduced with the MR damper. A reasonable agreement between the results obtained from the numerical analysis and those from the shaking table tests is also observed. On the other hand, tests conducted at different earthquake excitations and various excitation levels demonstrate the ability of the MR damper to surpass the performance of a comparable passive system in a variety of situations. Copyright © 2003 John Wiley & Sons, Ltd. [source]

On the accuracy of simplified methods for the analysis of isolated bridges

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 3 2001
P. Franchin
Abstract To foster the use of seismic isolation in structures, existing guidelines strive to formulate design methods which are simple and accessible to non-specialized engineers. On the other hand, not all of the simplifying provisions adopted by the norms can be said to have been adequately tested to provide a consistent level of accuracy. The study attempts, in particular, to elucidate three aspects related to the methods of analysis for linear or linearized isolated bridges on which little or no advice can be found in the norms. The first one is about the way one has to account for the fact that damping matrices of isolated bridges are never of proportional type. The present study demonstrates, through a number of typical applications, that classical modal analysis, using real modes and the diagonal terms of the modal damping matrices, still provide a fully acceptable approximation. The second and third aspects are related to the use of linearization expressions extended to the analysis of hyperstatic bridges. Parametric analyses conducted in the study show that none of the formulas in current use gives satisfactory results for both the displacement and the force responses, a requirement for a reliable design of an isolated bridge. How to use the equivalent linear parameters, and in particular the isolators equivalent damping ratios, in the context of a modal analysis, is treated next. This problem is seldom if ever mentioned in the norms where at most a formula is given for constructing modal damping ratios based on the damping ratios of the isolators. A rational, approximate procedure is discussed in this paper, applicable to all types of structures with non-proportional damping, which in the case of bridges can be shown to reduce to the expression provided in the Japanese bridge design guidelines. Copyright © 2001 John Wiley & Sons, Ltd. [source]

State-space time integration with energy control and fourth-order accuracy for linear dynamic systems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006
Steen Krenk
Abstract A fourth-order accurate time integration algorithm with exact energy conservation for linear structural dynamics is presented. It is derived by integrating the phase-space representation and evaluating the resulting displacement and velocity integrals via integration by parts, substituting the time derivatives from the original differential equations. The resulting algorithm has an exact energy equation, in which the change of energy is equal to the work of the external forces minus a quadratic form of the damping matrix. This implies unconditional stability of the algorithm, and the relative phase error is of fourth-order. An optional high-frequency algorithmic damping is constructed by optimal combination of three different damping matrices, each proportional to either the mass or the stiffness matrix. This leads to a modified form of the undamped algorithm with scalar weights on some of the matrices introducing damping of fourth-order in the frequency. Thus, the low-frequency response is virtually undamped, and the algorithm remains third-order accurate even when algorithmic damping is included. The accuracy of the algorithm is illustrated by an application to pulse propagation in an elastic medium, where the algorithmic damping is used to reduce dispersion due to the spatial discretization, leading to a smooth solution with a clearly defined wave front. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Operator-splitting method for real-time substructure testing

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 3 2006
Bin Wu
Abstract It has been shown that the operator-splitting method (OSM) provides explicit and unconditionally stable solutions for quasi-static pseudo-dynamic substructure testing. However, the OSM provides only an explicit target displacement but not an explicit target velocity, so that it is essentially an implicit method for real-time substructure testing (RST) when the velocity-dependent restoring force is considered. This paper proposes a target velocity formulation based on the forward difference of the predicted displacements so as to render the OSM explicit for RST. The stability and accuracy of the resulting OSM-RST algorithm are investigated. It is shown that the OSM-RST is unconditionally stable so long as the non-linear stiffness and damping are of the softening type (i.e. the tangent stiffness and damping never exceed the initial values). The stability of the OSM-RST for structures with infinite tangent damping coefficient or stiffness is also proved, and the stability of the method for MDOF structures with a non-classical damping matrix is demonstrated by an energy criterion. The effects of actuator delay and compensation are analysed based on the bilinear approximation of the actuator step response. Experiments on damped SDOF and MDOF structures verify that the stability of the OSM-RST is preserved when the experimental substructure generates velocity-dependent reaction forces, whereas the stability of real-time substructure tests based on the central difference method is worsened by the damping of the specimen. Copyright © 2005 John Wiley & Sons, Ltd. [source]